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Chapter 2: Problem 82

Calculate the concentration of a solution obtained by mixing \(300 \mathrm{~g}\) \(25 \%\) by weight solution of \(\mathrm{NH}_{4} \mathrm{Cl}\) and \(150 \mathrm{~g}\) of \(40 \%\) by weight solution of \(\mathrm{NH}_{4} \mathrm{Cl}\)

Short Answer

Expert verified
The concentration of NH4Cl in the mixture is approximately 30%.

Step by step solution

01

- Calculate the mass of NH4Cl in each solution

First, find the mass of NH4Cl in each solution by multiplying the total mass of the solution by the percentage concentration (in decimal form). For the 300 g of 25% solution: mass of NH4Cl = 300 g * 0.25. For the 150 g of 40% solution: mass of NH4Cl = 150 g * 0.40.
02

- Find the total mass of NH4Cl

Add the masses of NH4Cl from both solutions to get the total mass of NH4Cl in the mixture. Total mass of NH4Cl = (300 g * 0.25) + (150 g * 0.40).
03

- Calculate the total mass of the mixture

The total mass of the mixture is simply the sum of the masses of the two solutions. Total mass of mixture = 300 g + 150 g.
04

- Calculate the percentage concentration of NH4Cl

The concentration of NH4Cl in the mixture is the total mass of NH4Cl divided by the total mass of the mixture, multiplied by 100 to get the percentage. Percentage concentration = (Total mass of NH4Cl / Total mass of mixture) * 100.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Solution Preparation
Preparing a solution involves mixing a solute (the substance to be dissolved) with a solvent (the liquid in which the solute is dissolved). An essential part of solution preparation is the determination of the solute's concentration within the solvent. This ensures that the final solution has the correct properties for its intended use, whether in chemical analysis, medicine, or various industrial applications. When mixing solutions of the same solute, as in our exercise example, one must consider the masses and the concentration percentages of each original solution to obtain the desired concentration in the final mixture.
Percentage Concentration
Percentage concentration is a widely used way of expressing the concentration of a component in a mixture or solution. It's defined as the mass of the solute divided by the total mass of the solution, multiplied by 100 to give a percentage. This gives a straightforward understanding of how much solute is present relative to the solution as a whole. It's important to remember that the percentage is often based on weight, especially in solid-liquid mixtures. For instance, if you have a 25% by weight solution, this means there are 25 grams of the solute in every 100 grams of the total solution.
Mixture of Solutions
When mixing two solutions containing the same solute, the final concentration can be calculated by combining the masses of the solute from each starting solution. It's crucial to understand that the volume of the mixture might not be additive due to volume contraction. However, because the mass of substances is not lost in the mixing process, we can add the masses of the solute from the individual solutions directly to find the total mass of the solute in the final mixture. Thus, to calculate the concentration of the mixture, we take the combined mass of the solute and divide it by the total mass of the mixture, turning it into a percentage if needed.
Molar Concentration
Molar concentration, also known as molarity, is another common measure of solution concentration. It is defined as the number of moles of solute per liter of solution. The mole is a standard unit in chemistry that quantifies the amount of substance. To find the molar concentration, you first need to convert the mass of the solute into moles by using its molar mass, then divide by the volume of the solution in liters. Molarity is particularly important in reactions where the reacting volumes or the stoichiometry of the reactants are considered, as it allows chemists to calculate the exact amount of reactants needed for chemical reactions.

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Most popular questions from this chapter

(a) When \(4.2 \mathrm{~g} \mathrm{NaHCO}_{3}\) is added to a solution \(\mathrm{of} \mathrm{CH}_{3} \mathrm{COOH}\) weighing \(10.0 \mathrm{~g}\), it is observed that \(2.2 \mathrm{~g} \mathrm{CO}_{2}\) is released into atmosphere. The residue is found to weigh \(12.0 \mathrm{~g}\). Show that these observations are in agreement with the low of conservation of weigh. (b) If \(6.3 \mathrm{~g}\) of \(\mathrm{NaHCO}_{3}\) are added to \(15.0 \mathrm{~g} \mathrm{CH}_{3} \mathrm{COOH}\) solution. The residue is found to weigh \(18.0 \mathrm{~g}\). What is the mass of \(\mathrm{CO}_{2}\) released in this reaction.

Calculate the amount of oxalic acid \(\left(\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4} \cdot 2 \mathrm{H}_{2} \mathrm{O}\right)\) required to obtain \(250 \mathrm{~mL}\) of deci-molar solution.

Find the milli-cquivalent of : (a) \(\mathrm{Ca}(\mathrm{OH})_{2}\) in \(111 \mathrm{~g}\). (b) \(\mathrm{NaOH}\) in \(30 \mathrm{~g}\), (c) \(\mathrm{H}_{2} \mathrm{SO}_{4}\) in \(4.9 \mathrm{~g}\).

Find the normality of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) having 50 milli- equivalents in 3 litre.

Calculate the percentage composition in terms of mass of a solution obtained by mixing \(300 \mathrm{~g}\) of a \(25 \%\) and \(400 \mathrm{~g}\) of a \(40 \%\) solution by mass.
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